Left: HoAgGe single crystal. Right: anomalous Hall effect as function of the magnetic field B during up- and down sweeps (red / black) with right- (yellow) and left (green) rotating magnetic moment configurations.
Electrical currents and magnetic forces are directly liked to each other: current carrying cables create a circular magnetic field and vice versa a magnetic field deflects electrically charged particles perpendicular to the current and to the field direction. The latter phenomenon is called “Hall effect” in honor of its inventor Edwin Hall in the 19th century. Hall effect is used to probe electric and magnetic properties of metals. The “normal Hall effect” allows to determine the concentration of charger carriers and their mobility while an additional contribution labeled “anomalous Hall effect” arises in Magnets.
At the Institute of Physics at the University of Augsburg it has now been found that the anomalous Hall effect could reveal a hidden symmetry. “Despite an equal magnetization, two states show distinctly different anomalous Hall signals, a surprising and striking observation“, explains Philipp Gegenwart, Professor for Experimental Physics.
Right- and left-circulating magnetic pattern
The investigations were done with the magnetic metal HoAgGe, in which four years back, also at the chair of Prof. Gegenwart, special magnetic properties were discovered. The material features a triangular configuration of atomic electron spins of Holmium atoms. Since it is impossible to simultaneously fulfill all the pairwise interactions on each triangle, a magnetically frustrated state emerges. It features several energetically degenerate configurations per triangle and is called Kagome spin ice. The name indicates that the spins are located at the edges of corner shared triangles resembling braided Japanese “Kagome” baskets and furthermore that similar rules as in water ice determine the possible configurations of the magnetic moments.
In contrast to ordinary magnets, the magnetic moments in Kagome spin ice are not aligned along one direction but rather obey complex chiral pattern, i.e. with differing sense of rotation. They are created in an applied magnetic field at low temperatures and feature fractionalized magnetization plateaus at values of 1/3 and 2/3. The figure displays two of such pattern with similar energy and 1/3 of the saturation magnetization, each.
Electrical measurements uncover the difference – possible application for data storage
The study of the research group at the University of Augsburg systematically investigated and analyzed the anomalous Hall effect at low temperatures. Surprisingly, different values of the anomalous Hall effect were found for the two pattern of 1/3 magnetization, visible as red and black curves in the plot.
Modelling of the data revealed an underlying unique hidden symmetry: the combination of a 180° rotation and a distortion reversal is required for transforming one pattern into the other one. Conduction electrons scattering off the two different pattern get different curvatures of the phase of their wave functions and this leads to a difference in the anomalous Hall effect, despite a similar energy and magnetization of the two different pattern.
More generally, this observation indicates a new potential of measurements of the anomalous Hall effect in magnetically frustrated metals, for uncovering hidden symmetry and states through electrical measurements. “This may also be interesting with respect of permanent magnetic data storage at smallest atomic scale”, says Prof. Dr. Philipp Gegenwart. However, this requires the local addressing and selective switching of the sense of the rotation of these pattern.
Contact for scientific information:
Prof. Dr. Philipp Gegenwart
Dr. Kan Zhao
Experimentalphysik VI: Elektronische Korrelationen und Magnetismus
Telefon: +49 821 598 - 3650
E-Mail: philipp.gegenwart@physik.uni-augsburg.de
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Original publication:
K. Zhao, Y. Tokiwa, H. Chen und P. Gegenwart "Discrete degeneracies distinguished by the anomalous Hall effect in a metallic kagome ice compound", Nature Physics (2024), www.nature.com/articles/s41567-023-02307-w
